Mathematics

# $\displaystyle\int^{1}_{-1}x^3(1-x^2)dx=?$

$0$

##### SOLUTION

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int {\dfrac{dx}{\sin^2x \cos^2x}}$
• A. $\tan x-x+1$
• B. $\tan x-x$
• C. $\tan x+x$
• D. $\tan x-\cot x+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int\dfrac{dx}{(x + 100)\sqrt{x + 99}} = f(x) + c \Longrightarrow f(x) =$
• A. $2(x + 100)^{1/2}$
• B. $3(x + 100)^{1/2}$
• C. $2 \tan^{-1}(\sqrt{x + 100})$
• D. $2 \tan^{-1}(\sqrt{x + 99})$

1 Verified Answer | Published on 17th 09, 2020

Q3 Multiple Correct Hard
If $\displaystyle \int \frac {xe^x}{\sqrt {1 + e^x}} dx = f(x) \sqrt {1 + e^x} -2 \log \: g(x) + C$, then
• A. $\displaystyle f(x) = x - 1$
• B. $\displaystyle g(x) = \frac {\sqrt {1 + e^x} + 1}{\sqrt {1 + e^x} - 1}$
• C. $\displaystyle g(x) = \frac {\sqrt {1 + e^x} - 1}{\sqrt {1 + e^x} + 1}$
• D. $\displaystyle f(x) = 2(x - 2)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { \cfrac { 2x-1 }{ { \left( x-1 \right) }^{ 2 } } } dx\quad \quad$

$\int {\dfrac {\cos 2x}{\sin x}}dx$